Q8 of 32 Page 6

In Fig. 6.21, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR.Show that BC || QR.

(CBSE 2002, 2005)

To Prove: BC ll QR

Given that in triangle POQ, AB parallel to PQ

Hence,

Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.

(Basic proportionality theorem)


Now,


Therefore,

Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.

Using Basic proportionality theorem, we get:



From above equations, we get



BC is parallel to QR (By the converse of Basic proportionality theorem)

Hence, Proved.

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